Re: Wierd Truth Table

Protoman wrote:

I was playing around with prop logic and I made this strange truth
table:


P1 P2 C
A B A->B ~B Therefore ~A
---------------------------------------------
1 1 1 0 0
0 1 1 0 1
1 0 0 1 0
0 0 1 1 1

Apparently, it's impossible to get a case where the premises are both
false...at all!!!!!!!!! And what's even stranger is P1=1 and P2=0 shows
up twice!!!! And C is different in both!!!!!! that Is this some wierd
absurdity in prop logic, or did I make an error? Could you show me an
example of this argument in English? Thanks!!!!!!!!

NB: P1 and P2 are premises; C is the conclusion

The question is why is not possible that "A->B" and "notB" are
simultaneously false.

Suppose that A->B and not B are simultaneously false. Then B is true and,
consequently the consequent of A->B is true and so the entire A->B is true,
versus Hipothesis.

Therefore is not possible that notB and A->B are simultaneously false.

Roberto Vescarelli
.